Products of Independent Gaussian Random Matrices

Abstract

This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary matrix dimension and for an arbitrary number of factors. These exact results are used to study asymptotic limits for the macroscopic densities and the microscopic correlations as either the matrix dimension or the number of factors tends to infinity.

PhD thesis, Bielefeld University, 144 pages, 10 figures

References in corpus (20)

• Recent exact and asymptotic results for products of independent random matrices
• Singular value statistics of matrix products with truncated unitary matrices
• The Cauchy two-matrix model
• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Random matrices beyond the Cartan classification
• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Products of independent elliptic random matrices
• Universal distribution of Lyapunov exponents for products of Ginibre matrices
• Large N_c confinement and turbulence
• Energy correlations for a random matrix model of disordered bosons
• Universality conjecture and results for a model of several coupled positive-definite matrices
• Local universality in biorthogonal Laguerre ensembles
• Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for product of two Gaussian matrices
• Muttalib--Borodin ensembles in random matrix theory --- realisations and correlation functions
• Non-Hermitian extensions of Wishart random matrix ensembles
• Real eigenvalues of non-Gaussian random matrices and their products
• Bulk and soft-edge universality for singular values of products of Ginibre random matrices
• Supersymmetry for Products of Random Matrices
• Spectral Radii of Large Non-Hermitian Random Matrices
• Symplectic Structure of the Real Ginibre Ensemble

Cited by in corpus (14)

• Barren plateaus in quantum neural network training landscapes
• Statistical limits of dictionary learning: random matrix theory and the spectral replica method
• Hard edge limit of the product of two strongly coupled random matrices
• Matrix product ensembles of Hermite-type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral
• On Products of Random Matrices
• Precise characterization of the prior predictive distribution of deep ReLU networks
• Mixed Moments for the Product of Ginibre Matrices
• Real eigenvalue statistics for products of asymmetric real Gaussian matrices
• Limiting Empirical Spectral Distribution for Products of Rectangular Matrices
• The Product of Gaussian Matrices is Close to Gaussian
• Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles
• Spectral Radii of Products of Random Rectangular Matrices
• How many eigenvalues of a product of truncated orthogonal matrices are real?
• Product of Non-Hermitian Random Matrices